Prediction of influential proteins and enzymes of certain diseases using a directed unimodular hypergraph

Sathyanarayanan Gopalakrishnan; Swaminathan Venkatraman; Sathyanarayanan Gopalakrishnan; Swaminathan Venkatraman

doi:10.3934/mbe.2024015

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 325-345. doi: 10.3934/mbe.2024015

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Prediction of influential proteins and enzymes of certain diseases using a directed unimodular hypergraph

Sathyanarayanan Gopalakrishnan ¹,
Swaminathan Venkatraman ^{2
,
,}

1.
Department of Mathematics, Srinivasa Ramanujan Centre, School of Arts, Sciences, Humanities and Education, SASTRA Deemed University, Thanjavur, India
2.
Department of Mathematics, School of Arts, Sciences, Humanities and Education, SASTRA Deemed University, Thanjavur, India

Academic Editor: Frank Werner

Received: 12 August 2023 Revised: 16 November 2023 Accepted: 22 November 2023 Published: 13 December 2023

Protein-protein interaction (PPI) analysis based on mathematical modeling is an efficient means of identifying hub proteins, corresponding enzymes and many underlying structures. In this paper, a method for the analysis of PPI is introduced and used to analyze protein interactions of diseases such as Parkinson's, COVID-19 and diabetes melitus. A directed hypergraph is used to represent PPI interactions. A novel directed hypergraph depth-first search algorithm is introduced to find the longest paths. The minor hypergraph reduces the dimension of the directed hypergraph, representing the longest paths and results in the unimodular hypergraph. The property of unimodular hypergraph clusters influential proteins and enzymes that are related thereby providing potential avenues for disease treatment.
- directed hypergraph,
- unimodular hypergraph,
- path,
- depth first search,
- protein protein interactions
Citation: Sathyanarayanan Gopalakrishnan, Swaminathan Venkatraman. Prediction of influential proteins and enzymes of certain diseases using a directed unimodular hypergraph[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 325-345. doi: 10.3934/mbe.2024015

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Abstract

Protein-protein interaction (PPI) analysis based on mathematical modeling is an efficient means of identifying hub proteins, corresponding enzymes and many underlying structures. In this paper, a method for the analysis of PPI is introduced and used to analyze protein interactions of diseases such as Parkinson's, COVID-19 and diabetes melitus. A directed hypergraph is used to represent PPI interactions. A novel directed hypergraph depth-first search algorithm is introduced to find the longest paths. The minor hypergraph reduces the dimension of the directed hypergraph, representing the longest paths and results in the unimodular hypergraph. The property of unimodular hypergraph clusters influential proteins and enzymes that are related thereby providing potential avenues for disease treatment.

References

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